Effect Of Time-Delay On Holling Ⅱ Function Predator-Prey System With Incubation Period

In this thesis, we add to the predator containing the latent period of infectious disease on the basis of previous studies. It is in order to make the model further improvement. In this article, we consider that predators during the latency of disease and the outbreak of infectious disease in Holling Ⅱfunctional period by the impact of time delay in the predator-prey system. In the first part of the article, we discuss the existence of the equilibrium conditions by using a variety of stability criteria. On the stability of the equilibrium points in the system are determined, the existence of Hopf bifurcation in the time-delay exists when the conditions are obtained. In the second part of the article, we judge and analysis the directionality and periodic solution of Hopf bifurcation. At last, we use data to analyse the equilibriums of system obtained, and we apply MATLAB software tool to draw some balance in the conditions of stability and instability image conditions.